Extending Coinductive Logic Programming with Co-Facts

TL;DR

This paper introduces co-facts into logic programming to better handle predicates on non-well-founded structures, unifying inductive and coinductive paradigms with a new fixed point semantics.

Contribution

It extends coinductive logic programming with co-facts, allowing more precise definitions for infinite structures and unifying inductive and coinductive reasoning.

Findings

Defines a new fixed point semantics influenced by co-facts

Provides declarative and operational semantics with correctness proofs

Develops a prototype meta-interpreter demonstrating the paradigm

Abstract

We introduce a generalized logic programming paradigm where programs, consisting of facts and rules with the usual syntax, can be enriched by co-facts, which syntactically resemble facts but have a special meaning. As in coinductive logic programming, interpretations are subsets of the complete Herbrand basis, including infinite terms. However, the intended meaning (declarative semantics) of a program is a fixed point which is not necessarily the least, nor the greatest one, but is determined by co-facts. In this way, it is possible to express predicates on non well-founded structures, such as infinite lists and graphs, for which the coinductive interpretation would be not precise enough. Moreover, this paradigm nicely subsumes standard (inductive) and coinductive logic programming, since both can be expressed by a particular choice of co-facts, hence inductive and coinductive predicates can coexist in the same program. We illustrate the paradigm by examples, and provide declarative and operational semantics, proving the correctness of the latter. Finally, we describe a prototype meta-interpreter.